18.3 Content
18.3.1 The Ray Model of Light
In ray optics, we model light as straight lines (rays) that travel in uniform media and change direction at boundaries.
Key assumptions: - Light travels in straight lines - Rays are perpendicular to wavefronts - Valid when obstacles are much larger than wavelength
18.3.2 Reflection
The law of reflection states:
\[\theta_i = \theta_r\]
- Angle of incidence (\(\theta_i\)): Angle between incident ray and normal
- Angle of reflection (\(\theta_r\)): Angle between reflected ray and normal
- The normal is perpendicular to the surface
18.3.3 Interactive: Reflection from a Plane Mirror
18.3.4 Refraction and Snell’s Law
Refraction occurs when light crosses a boundary between two media with different optical densities.
Snell’s Law: \[n_1 \sin\theta_1 = n_2 \sin\theta_2\]
where \(n\) is the refractive index of each medium.
The refractive index measures how much light slows down in a medium: \[n = \frac{c}{v}\] where \(c\) is the speed of light in vacuum and \(v\) is the speed in the medium.
18.3.5 Common Refractive Indices
| Material | Refractive Index (\(n\)) |
|---|---|
| Vacuum | 1.00 (exactly) |
| Air | 1.00 (approximately) |
| Water | 1.33 |
| Glass | 1.50 (typical) |
| Diamond | 2.42 |
18.3.6 Interactive: Refraction at a Boundary
Light bending as it enters a denser medium:
Key observation: Light bends toward the normal when entering a denser (higher \(n\)) medium.
18.3.7 Total Internal Reflection
When light travels from a denser to a less dense medium, there exists a critical angle \(\theta_c\) beyond which all light is reflected internally.
\[\sin\theta_c = \frac{n_2}{n_1}\]
Total internal reflection is used in: - Optical fibres (telecommunications) - Prisms in binoculars - Endoscopes (medical imaging)
18.3.8 Thin Lens Equation
For thin lenses, the object distance (\(u\)), image distance (\(v\)), and focal length (\(f\)) are related by:
\[\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\]
Sign conventions:
- Real objects: \(u > 0\) (in front of lens)
- Real images: \(v > 0\) (on opposite side from object)
- Virtual images: \(v < 0\) (same side as object)
- Converging lens: \(f > 0\)
- Diverging lens: \(f < 0\)
18.3.9 Magnification
Magnification describes how the image size compares to the object size:
\[m = \frac{h_i}{h_o} = -\frac{v}{u}\]
- \(|m| > 1\): Image larger than object
- \(|m| < 1\): Image smaller than object
- \(m > 0\): Upright image
- \(m < 0\): Inverted image
18.3.10 Interactive: Converging Lens Ray Diagram
18.3.11 Real vs Virtual Images
| Property | Real Image | Virtual Image |
|---|---|---|
| Can be projected | Yes | No |
| Light rays | Actually converge | Appear to diverge from a point |
| Orientation | Inverted | Upright |
| Sign of \(v\) | Positive | Negative |